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Chapter 6 Supplemental Problems

Electrical Properties

1. What will be the resistance of a copper wire 0.08" in diameter and 100 ft. long if its resistivity is

1.7 microohm-cm?

2. A maximum resistance of 1 ohm is permitted in a copper wire 25 ft long. What is the smallest

wire diameter which can be used?

3. What is the electrical conductivity of iron (a) at room temperature? (b) at 212 /F?

4. Silicon has a density of 2.40 g/cc. (a) What is the concentration of the silicon atoms per cubic

centimeter? (b)5. Phosphorus is added to the silicon to make it an n-type semiconductor with a conductivity of 1

mho/cm and an electron mobility of 1700 cm2/volt-sec. What is the concentration of the

conduction electrons per cubic centimeter?

6. (a) How many silicon atoms are there for each conduction electron in the above problem? (b)

The lattice constant for silicon is 5.42 D, and there are 8 atoms per unit cell. What is the volume

associated with each conduction electron?

7. Germanium used for transistors has a resistivity of 2 ohm-cm and an electron "hole"

concentration of 1.9 x 1015 holes/cc. (a) What is the mobility of the electron holes in the

germanium? (b) What impurity element could be added to germanium to create electron holes?

8. Calculate the mobility of electrons in Cu. The resistivity of Cu is 1.72 x 10-8 ohm-m at 25/C and

its density is 8.9 g/cc. Assume each copper atom donates one valence electron to the conductionband.

9. Define a conductor, semi-conductor and insulator in terms of the energy band model.

10. What is the relation for conducting materials of the resistivity and temperature? Give a

qualitative explanation for the three regions of temperature dependence in terms of the two

contributions of resistivity.

11. Explain the factors affecting the electrical resistivity of metals.

12. (a) Compute the electrical conductivity of a 5.1-mm (0.2-in.) diameter cylindrical silicon

specimen 51 mm (2 in.) long in which a current of 0.1 A passes in an axial direction. A voltage

of 12.5 V is measured across two probes that are separated by 38 mm (1.5 in.). (b) Compute the

resistance over the entire 51 mm (2 in.) of the specimen.

13. An aluminum wire 4 mm in diameter is to offer a resistance of no more than 2.5 S. Look up datafor aluminum and compute the maximum wire length.

14. At room temperature the electrical conductivity and the electron mobility for copper are 6.0

107 (S-m)-1 and 0.0030 m2/V-s, respectively. (a) Compute the number of free electrons per cubicmeter for copper at room temperature. (b) What is the number of free electrons per copper atom?

Assume a density of 8.9 g/cm3.

Answers for Electrical Properties

1. 0.16 ohm.

2. 0.016 in (0.04 cm).

3. (a) 105 mho/cm; (b) 6 x 104 mho/cm.

4. (a) 5.15 x 1022 atoms/cc; (b) 3.68 x 1015 carrier electrons/cc.6. (a) 1.4 x 107 silicon atoms per conduction electron (also 1.4 x 107 silicon atom per phosphorus atom);

(b) (655 D)3.

7. (a) 1600 cm2/vol-sec; (b) Al, In, Ga.

8. 4.33 x 10-3 m2/V-s

12. (a) 14.9 (S-m)-1

13. 1195 m

14. (b) 1.48

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Magnetic Properties

1. A coil of wire 0.20 m long and having 200 turns carries a current of 10 A. (a) What is the

magnitude of the magnetic field strength H? (b) Compute the flux densityB if the coil is in a

vacuum. (c) Compute the flux density inside a bar of titanium that is positioned within the coil.

(d) Compute the magnitude of the magnetization M.

2. The magnetic flux density within a bar of some material is 0.435 tesla at anHfield of 3.44 105

A/m. Compute the following for this material: (a) the magnetic permeability, and (b) the

magnetic susceptibility. (c) What type(s) of magnetism would you suggest as being displayed by

this material? Why?3. Compute (a) the saturation magnetization and (b) the saturation flux density for cobalt, which

has a net magnetic moment per atom of 1.72 Bohr magnetons and a density of 8.90 g/cm3.

4. The chemical formula for manganese ferrite may be written as (MnFe2O4)8 because there are

eight formula units per unit cell. If this material has a saturation magnetization of 5.6 105 A/m

and a density of 5.00 g/cm3, estimate the number of Bohr magnetons associated with each Mn2+

ion.

5. The following data are for a transformer steel:

H(A/m) B (teslas)

0 0

10 0.03400 1.28

20 0.07

600 1.36

50 0.23

800 1.39

100 0.70

1000 1.41

150 0.92

200 1.04

(a) Construct a graph ofB versus H. (b) What are the values of the initial permeability and initial

relative permeability? (c) What is the value of the maximum permeability? (d) At about whatHfield

does this maximum permeability occur? (e) To what magnetic susceptibility does this

maximum permeability correspond?

Answers

1. (a) 10,000 A-turns/m (b) B0 = 1.257 10-2 Tesla; (c) B ~ 1.257 10-2 Tesla; (d) M= 1.81 A/m

2. (a) ~ 1.26 10-6 H/m; Pm = 6 10-3

3. (a) Ms = 1.45 106 A/m

4. 4.6 Bohr magnetons/Mn2+ ion

5. (a) i = 3.0 10-3 H/m, ri = 2400; (b) (max) = ~ 9 10

-3 H/m

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Optical Properties

1. Compute the velocity of light in calcium fluoride (CaF2 ), which has a dielectric constant ,r of

2.056 (at frequencies within the visible range) and a magnetic susceptibility of -1.43 10-5.

2. The fraction of nonreflected radiation that is transmitted through a 10-mm thickness of a

transparent material is 0.90. If the thickness is increased to 20 mm, what fraction of light will be

transmitted?

3. The transmissivity Tof a transparent material 20 mm thick to normally incident light is 0.85. If

the index of refraction of this material is 1.6, compute the thickness of material that will yield a

transmissivity of 0.75. All reflection losses should be considered.

Answers

1. v = 2.09 108 m/s

2. IT/I0 = 0.81

3. l= 67.3 mm

Thermal Properties (Note: some of this is covered in previous chapters)

1. For aluminum, the heat capacity at constant volume Cv at 30 K is 0.81 J/mol-K, and the Debye

temperature is 375 K. Estimate the specific heat (a) at 50 K and (b) at 425 K.

2. An aluminum wire 10 m (32.8 ft) long is cooled from 38 to 1C. How much change in length

will it experience?3. To what temperature must a cylindrical rod of tungsten 10.000 mm in diameter and a plate of

316 stainless steel having a circular hole 9.988 mm in diameter have to be heated for the rod to

just fit into the hole? Assume that the initial temperature is 25C.

Answers

1. (a) Cv = 139 J/kg-K; (b) Cv = 925 J/kg-K

2. )l= -9.2 mm3. Tf= 129.5 C